Numerators and Denominators in Addition

Date: 3/3/96 at 9:46:30
From: "David P. Lovett"
Subject: adding fractions

Why do we add numerators but not denominators when we add 
fractions with like denominators?

Date: 3/4/96 at 21:55:45
From: Doctor Ken
Subject: Re: adding fractions

Hello!

The answer to your question can actually be seen by looking at 
the English language, of all things!  Let's say we have 3 
oranges, and we add that to 5 oranges.  What do we get?  We get 
8 oranges.  We DON'T get 8 (oranges+oranges).  That would be 
pretty weird.

Well, the situation is just the same with fractions.  If we're 
adding 3/11 + 5/11, we're not adding oranges any more, we're 
adding these things called "elevenths."  This fact is reflected 
in how we say this sentence:"3 elevenths plus 5 elevenths equals 
8 elevenths."If we replace "elevenths" with "oranges," we get 
the same kind of thing: "3  oranges  plus 5  oranges  equals 8  
oranges." So that's why.  Here's a question for you: why do we 
need a common denominator in the first place?

-Doctor Ken,  The Math Forum